The 9/11 Memorial foundation, funded to the tune of $830 million, has begun nickel-and-diming visitors for ticket reservations.

Even though the nonprofit has long vowed admission to the sacred site would be free, it is now demanding $2 per ticket for all advance reservations made online or by phone.

Officials quietly rolled out the fee on March 1 – but it did not escape the notice of some outraged families of Sept. 11 victims.

“I don’t want the American public to have to pay a dime to pay respects to my son,” said Sally Regenhard, whose firefighter son, Christian, died in the World Trade Center attacks.

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“They made . . . a vow that no one would ever be charged for going to the memorial, but money is the bottom line here,” she fumed.

“They’re making money off the people that died. It’s disgusting,” said Jim Riches, a retired FDNY deputy chief who lost his firefighter son, Jimmy, on 9/11.

“The memorial should be free for everybody to pay their respects. You wouldn’t charge money to get into a cemetery.”

According to the memorial’s Web site, the booking fees are necessary to “safely manage visitor capacity” while surrounding construction projects are completed.

The nonprofit claims on its Web site that it “does not receive city, state or federal funding for its operations.”

But from 2006 to 2011, it pulled in about $295 million in taxpayer-funded grants for construction.

It also reaped more than $430 million in private donations after the tragedy, including pennies raised by millions of patriotic American schoolchildren.

“Like other similar institutions, in order to help support the operational needs of the 9/11 Memorial, we have implemented a service fee, solely for advance reservations,” foundation CEO Joe Daniels told The Post.

The memorial compares it to the American Museum of Natural History’s $2 charge and the Washington Monument’s $1.50 reservation fee.

But critics are calling it a two-bit money grab by fat cats hemorrhaging funds. Construction costs are now pegged at $700 million for the museum and memorial – more than it took to build the Empire State Building.

The foundation, chaired by Mayor Bloomberg, says the memorial and museum will cost $60 million a year to operate once complete. Security will cost $12 million a year, and another $5 million will go to operating the waterfall tributes.

Add that to the nonprofit’s swanky salaries: Ten of the 12 directors raked in more than $200,000 in 2011. Daniels pulled down $336,224 in salary and benefits, and Museum Director Alice Greenwald made $351,171, tax filings show.

One former employee, Joan Gerner, got a $300,000 severance after leaving the foundation – on top of her $439,463 salary.

The memorial opened in 2011 and has attracted 7 million visitors. It features two enormous reflecting pools set within the footprints of the Twin Towers and takes up half the 16-acre WTC site.

Construction on the underground museum ground to halt in late 2011 after the Port Authority, which owns the land, claimed the nonprofit owed $300 million in cost overruns. Development restarted after both sides reached a deal last September.

How the memorial and museum will foot its bills remains unclear.

Daniels is mulling a $20 mandatory admission or a $25 suggested donation for the museum, similar to the Metropolitan Museum of Art, once it opens in 2014.

Visiting the memorial – a public plaza – will be free, eventually.

Memorial officials also want federal handouts, and are hoping to revive a Senate bill that would force the National Park Service to shell out $20 million a year.